Recall, with reference to FIG. 1a, the operating principle of a vibratory gyroscope.
A mass M is suspended on a rigid frame C by means of two springs of stiffness Kx and Ky. It therefore has two degrees of freedom along the x and y directions, perpendicular to each other and lying in the plane of the figure.
The system may be considered as a conjunction of two resonators of eigenfrequency Fx along x and Fy along y.
The mass M is driven along the x-axis at a frequency f and with a constant amplitude x0. This frequency is generally chosen to be equal to the eigenfrequency of the mode of vibration along x. The acceleration of the mass M along x, called the drive acceleration, is then of the form:Γexcx=−ω2x0 sin(ωt) with ω=2πf 
In the presence of a rotation speed Ω around the third axis z, the Coriolis forces cause a coupling between the two resonators giving rise to a vibration of the mass along the y-axis, often called the sense axis. An acceleration, called Coriolis acceleration, appears along the y-axis:Γcorx=2Ωωx0 cos(ωt)
The measurement of the rotation speed Ω is therefore made through measuring the movement along y caused by the Coriolis acceleration. In fact, the amplitude of the movement along y is proportional to the rotation speed Ω.
However, due to geometric imperfections in the mass, the x and y axes lack orthogonality as illustrated in FIG. 1b. Due to this nonorthogonality α, the acceleration along the sense axis y includes not only the Coriolis acceleration but also a component coming from the projection on y of the drive acceleration:Γy=2Ωωx0 cos(ωt)cos α−ω2x0 sin(ωt)sin α
Assuming that α is very small compared with 1, this yields:
      Γ    y    =      2    ⁢                  ⁢    ω    ⁢                  ⁢                  x        0            ⁡              (                              Ω            ⁢                                                  ⁢                          cos              ⁡                              (                                  ω                  ⁢                                                                          ⁢                  t                                )                                              -                      α            ⁢                          ω              2                        ⁢                          sin              ⁡                              (                                  ω                  ⁢                                                                          ⁢                  t                                )                                                    )            
Hence it is observed that an interference term αω/2 sin(ωt) is superposed on the term Ω cos(ωt) representing the useful information to be measured. This interference term, in phase quadrature with the useful term, is generally called quadrature error.
As the interference signal is in phase quadrature with the useful signal, it may be eliminated by demodulation. However, demodulation which is not perfect includes a phase error Δφ which introduces an error to the speed measurement:
      Ω    ⁢                  ⁢    mes    ≈      Ω    -          α      ⁢              ω        2            ⁢      Δϕ      
To obtain a stability of 10°/h in the speed measurement, the term
  α  ⁢      ω    2    ⁢  Δϕmust have a stability of 10°/h.
For a phase stability of 100 μrad (or 0.0057°) with a frequency ω=2π·10000 rad/s, the nonorthogonality α must therefore be less than 15 μrad in order to obtain a stability of 10°/h.
Geometric defects in the sensing element generally lead to a nonorthogonality of a few hundred microradians.
To obtain the sought precision in the speed measurement, it is therefore necessary to reduce the nonorthogonality, which amounts to compensating for the quadrature error. This process is often called balancing.
With equal stability performance on the speed measurement, the reduction in quadrature error also allows a relaxation in the necessary phase precision ΔΦ.
The balancing operation therefore has two objectives: to improve the precision in the speed measurement and/or relax the phase precision of the electronics.
A first method for carrying out the balancing or the orthogonalization of the drive and sense axes is to remove some material locally (laser ablation for example) so as to modify the distribution of mass or of the stiffness linked with the mass M. This method is generally expensive to implement and is difficult to apply to a micromachined planar vibratory gyroscope, the sensing and drive movements of which are situated in the plane of the substrate.
Another method consists in deforming the movable mass and possibly the stiffness elements of the sensing or drive movement in such a way that the drive and sensing movements become orthogonal. This static deformation may then be carried out by applying electrostatic forces to the mass or to its movable elements. This method is described, for example, in the Patent WO 2004/042324.
A final method consists in using an electrostatic field not to deform the stiffness elements as in the preceding method, but to modify the distribution of the stiffness of the system using an electrostatic stiffness. This type of method is currently employed on certain types of vibratory gyroscope such as vibrating ring or cup gyroscopes, but until now has never been implemented on micromachined planar vibratory gyroscopes, with a simple or double tuning fork, the sensing and drive movements of which are linear and situated in the plane of the substrate.